Related papers: Sampling Methods for Inner Product Sketching

Randomized sketching is currently introduced into every area of numerical linear algebra. In Krylov subspace methods, it allows runtime savings at the cost of small accuracy reductions. This work offers a different view on sketching in…

We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…

Many datasets such as market basket data, text or hypertext documents, and sensor observations recorded in different locations or time periods, are modeled as a collection of sets over a ground set of keys. We are interested in basic…

Embedding approaches have become one of the most pervasive techniques for multi-label classification. However, the training process of embedding methods usually involves a complex quadratic or semidefinite programming problem, or the model…

This article considers "compressive learning," an approach to large-scale machine learning where datasets are massively compressed before learning (e.g., clustering, classification, or regression) is performed. In particular, a "sketch" is…

We describe a general framework -- compressive statistical learning -- for resource-efficient large-scale learning: the training collection is compressed in one pass into a low-dimensional sketch (a vector of random empirical generalized…

The nowadays massive amounts of generated and communicated data present major challenges in their processing. While capable of successfully classifying nonlinearly separable objects in various settings, subspace clustering (SC) methods…

The estimation of coverage probabilities, and in particular of the missing mass, is a classical statistical problem with applications in numerous scientific fields. In this paper, we study this problem in relation to randomized data…

In the compressive learning theory, instead of solving a statistical learning problem from the input data, a so-called sketch is computed from the data prior to learning. The sketch has to capture enough information to solve the problem…

Sketching techniques have gained popularity in numerical linear algebra to accelerate the solution of least squares problems. The so-called $\varepsilon$-subspace embedding property of a sketching matrix $S$ has been largely used to…

By leveraging contrastive learning, clustering, and other pretext tasks, unsupervised methods for learning image representations have reached impressive results on standard benchmarks. The result has been a crowded field - many methods with…

Sketching is a randomized dimensionality-reduction method that aims to preserve relevant information in large-scale datasets. Count sketch is a simple popular sketch which uses a randomized hash function to achieve compression. In this…

It is often desirable to reduce the dimensionality of a large dataset by projecting it onto a low-dimensional subspace. Matrix sketching has emerged as a powerful technique for performing such dimensionality reduction very efficiently. Even…

This paper develops the sketching (i.e., randomized dimension reduction) theory for real algebraic varieties and images of polynomial maps, including, e.g., the set of low rank tensors and tensor networks. Through the lens of norming sets,…

In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new…

Datasets that are terabytes in size are increasingly common, but computer bottlenecks often frustrate a complete analysis of the data. While more data are better than less, diminishing returns suggest that we may not need terabytes of data…

Sketching is used as a ubiquitous tool of expression by novices and experts alike. In this thesis I explore two methods that help a system provide a geometric machine-understanding of sketches, and in-turn help a user accomplish a…

Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical…

Network stream mining is fundamental to many network operations. Sketches, as compact data structures that offer low memory overhead with bounded accuracy, have emerged as a promising solution for network stream mining. Recent studies…

In order to compute fast approximations to the singular value decompositions (SVD) of very large matrices, randomized sketching algorithms have become a leading approach. However, a key practical difficulty of sketching an SVD is that the…